Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

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Access Right: Closed AccessAuthor: search.filters.author.Temur, Faruk

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  • Article
    Random Exponential Sums and Lattice Points in Regions
    (Academic Press inc Elsevier Science, 2025) Temur, Faruk; Sahilliogullari, Cihan; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    In this article we study two fundamental problems on exponential sums via randomization of frequencies with stochastic processes. These are the Hardy-Littlewood majorant problem, and L2n(T), n is an element of N norms of exponential sums, which can also be interpreted as solutions of diophantine equations or lattice points on surfaces. We establish connections to the well known problems on lattice points in regions such as the Dirichlet divisor problem. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
  • Article
    Citation - Scopus: 1
    Level Set Estimates for the Discrete Frequency Function
    (Springer Verlag, 2019) Temur, Faruk; Temur, Faruk; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    We introduce the discrete frequency function as a possible new approach to understanding the discrete Hardy-Littlewood maximal function. Considering that the discrete Hardy-Littlewood maximal function is given at each integer by the supremum of averages over intervals of integer length, we define the discrete frequency function at that integer as the value at which the supremum is attained. After verifying that the function is well-defined, we investigate size and smoothness properties of this function.